\begin{tikzpicture}
    \pgfmathsetmacro{\R}{1.5}
    \tkzDefPoints{0/0/O}
    \tkzDefPoint(240:\R){A}
    \tkzDefRegPolygon[center,sides=6,name=P](O,A)
    \foreach \P [count=\i from 2] in {B,C,...,F} {
        \coordinate (\P) at (P\i);
    }

    \tkzDrawCircle[very thick](O,A)
    \tkzDrawPolygon[red, thick](A,...,F)
    \tkzDrawSegments(C,F)
    \tkzDrawArc(F,A)(E)
    \tkzDrawArc(C,D)(B)
    \tkzLabelPoints[above right](O)
    \tkzAutoLabelPoints[center=O, centered, dist= .25](A,B,...,F)
\end{tikzpicture}

% \begin{tikzpicture}
%     \pgfmathsetmacro{\R}{1.5}
%     \tkzDefPoints{0/0/O}
%     \tkzDefPoint(0:\R){C}
%     \tkzDefPoint(60:\R){D}
%     \tkzDefPoint(120:\R){E}
%     \tkzDefPoint(180:\R){F}
%     \tkzDefPoint(240:\R){A}
%     \tkzDefPoint(300:\R){B}

%     \tkzDrawCircle[very thick](O,A)
%     \tkzDrawPolygon[red, thick](A,...,F)
%     \tkzDrawSegments(C,F)
%     \tkzDrawArc(F,A)(E)
%     \tkzDrawArc(C,D)(B)
%     \tkzLabelPoints[above right](O)
%     \tkzLabelPoints[below left](A)
%     \tkzLabelPoints[below right](B)
%     \tkzLabelPoints[right](C)
%     \tkzLabelPoints[above right](D)
%     \tkzLabelPoints[above left](E)
%     \tkzLabelPoints[left](F)
% \end{tikzpicture}

